Greek Beginnings

Question 1

What is Thale’s Thorem

Answer 1

It states thats if a triangle is construted on the diameter of a circle (point A and B) then when point C is on the circumfrence will always be a 90 degree angle

Question 2

What is the Inscribed Angle Therom?

Answer 2

It states that if you create a trianlge with a circle, and you plot a second triangle the angle within the second triangle will be twice the anlge of second triangle

Question 3

Methods of proving that triangles are congruant?

Answer 3

AsA= Angle-side-Angle
SAS= Side-angle-side
SSS = side- side-side

Question 4

What is the pefect 5th?

Answer 4

Different ratios in music

Question 5

What are Figuartive numbers? Who created Introductio Arithmetica?

Answer 5

These are numbers thats are based of shapes. There are triangular shapes, Square numbers.

Nichomohi created Introductio Arithmetica

Question 6

Who founded the school at crotona, what were the types of students, and what were the four ideas of study?

Answer 6

Thales of mileto and Pyhogoes of Samos

The two types of students were Acousitici (people who hadn’t gained the right to talk about math yet. And the Mthematici, which were the members who could talk about these subjects.

The four main ideas of study were:

Arithemetica (Number theroy)
Harmonia Music
germoeroty; geometty
Astilogici; astronomy

Question 7

What are pythagorean triple numbers?

Answer 7

These are numbers that obey a^2+b^2=C^2

x=2n+1
x=2n^2+2n
z=2n^2+2n+a

Question 8

The Crisis of Incommensables

Answer 8

Irrational numbers weren not able to be expressed in any form such as ratios. For example sqrt(2) was famous number that wasn’t able to be show as a whole number or ratio.

Question 9

Ideas of Eudoxus

Answer 9

Theory of irrational # and treating them as lengths of a line sequence

Theory of real numbers

Theory of proportions/ratios

Golden ratio:
1+sqrt(5):1

Method of exhaustion: a greek way of dealing with limits

The area of a circle is proportional to diameter

A model of solar systems using geocenrtirc spheres

Question 10

What were the 3 impossible greek geometric constructions and what were the rules of them

Answer 10

Squaring a Circle
Doubling a cube
Trisecting an anlge

The greeks were only able to use a compass and unmarked strightedge

Question 11

Who Wrote ______ Physics and the Heavens

Answer 11

It was Aristole

Physics on earth consisted of change of any kind

-quantiative change
-qualtivite change
-Generation/corruption
-change of location
-local motion